Revising Feynman Diagrams

in OCDlast month

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Sigh... it has been a while since I've had to fiddle around with Feynman diagrams for visualising nuclear interactions in Physics. Well, I guess that is no surprise, as it isn't really something that pops up very often when you are playing Violin!

However, I currently have a student who is a bit more advanced in Physics and she has started using these diagrams. Most of the topics that I've covered with her in the past have been well within my comfort zone... however, I really should refresh my knowledge with these visualisation tools before I start leading her down the wrong path.

It shouldn't be too difficult, after all... they haven't changed in the past 50 or so years since Feynman introduced them as a way to visualise interactions, and we should be dealing with relatively simple ones. So, it should be like falling off a bike!

So, I have the above templates for a few Weak interaction vertices that I can use to piece together full diagrams.

(1) Down quark entering, up quark and negative W boson exiting.
(2) Electron entering, electron neutrino and negative W boson exiting.
(3) Muon entering, muon neutrino and negative W boson exiting.
(4) Electron entering, electron and neutral Z boson exiting.

With these vertices, I should be able to piece together a few nuclear reactions in visual form.

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So, this is the first of the diagrams. Time flows from Left to Right, arrows pointing in the direction of forward time are particles whilst arrows pointing in the reverse time direction are antiparticles (they don't go backwards in time, it is just a representation). Solid lines represent particles, and squiggly lines are virtual particles (the virtual bosons that are the force carriers, in this case for the weak force interaction).

This diagram represents a Muon decaying to an electron, electron anti-neutrino and muon neutrino. (I'm not hunting down the symbols in this text editor!)

Coming in from the left is the Muon into the first vertex. So, we take (3) and turn it so that the Muon is coming in horizontally, which decays to the muon neutrino and negative W boson. However, the W boson is virtual particle, so we can't finish here. Need to resolve to real particles.

Taking (2), we turn it until the W boson squiggly lines up with the exiting W boson from the first vertex. However, the direction of the arrow is opposite, so we need to reverse the arrows of all the lines leading to (2).

This results in the negative W boson (second vertex) decaying into an electron and an electron anti-neutrino. It is an anti-neutrino because the arrow is pointing in the reverse time direction.

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(B) describes a neutron decay (known as beta decay) into a proton, electron and electron anti-neutrino.

For this, we need to describe the quark structure of the two baryons (the neutron and proton). The neutron is (ddu) and results in a proton (uud), so... one of the down quarks changes into an up quark.

In our diagram, we track the two quarks (one d and one u) that DON'T CHANGE on the top. On the bottom, we trace the change from the down quark to the u quark.

For this, we use (1) and tilt until we have the down (d) quark coming in from the left, this forms our first vertex, with the up quark exiting the vertex to form the proton with the other two quarks, and the negative W boson continuing onwards.

Again, the virtual W needs to be resolved into real particles, and we use (2) to do this. Again, we need to tilt (2) to have the right orientation (the W boson coming inwards from the left) and again, we need to reverse the directions on the arrows to the vertex.

After doing this, we have the electron coming out of the second vertex in the forward time direction and the electron neutrino pointing in the reverse time direction... hence, an electron and an electron anti-neutrino.

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This next one should be pretty simple now. Describing an electron and electron anti-neutrino decaying to a Muon and muon anti-neutrino.

Coming in from the left, we use vertex (2). The directions of the arrows give the electron and electron anti-neutrino, with the negative W boson coming out. Resolve the virtual particle with (3), realigning the vertex and reversing the arrows. Resulting in the Muon, and muon anti-neutrino.

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Positive Kaon decay into anti-Muon and muon neutrino... using templates (1) and (3)

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Finally, this last one (E) had me a little bit stumped for a little. There were no strange quarks included for use in the templates, and the question did say that we could only use the templates to draw the Feynman diagrams. In the end, I had to cheat and look up a Strange Weak interaction vertex and use that as the first vertex.


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